Baseflow identification via explainable AI with Kolmogorov-Arnold networks

TL;DR

This paper introduces Kolmogorov-Arnold networks (KANs), a neural network approach for symbolic expression identification, demonstrating superior performance and interpretability in baseflow identification and water-balance modeling across US catchments.

Contribution

The paper presents a novel application of KANs for hydrological modeling, improving accuracy and simplicity over traditional methods and other machine learning models.

Findings

KAN-derived dependencies outperform original models in baseflow tasks

NSE increased by 67%, RMSE decreased by 30%, Kling-Gupta efficiency increased by 24%

Refined water-balance equations outperform current models with up to 105% NSE improvement

Abstract

Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov-Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN-derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts. On a test set, they increase the Nash-Sutcliffe Efficiency (NSE) by 67%, decrease the root mean squared error by 30%, and increase the Kling-Gupta efficiency by 24%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water-balance equation at the mean-annual scale. The KAN-derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN-derived equations based on the original water balance. While the performance of our model and tree-based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes.